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Method of Maximal Monotonic Operators in the Theory of Nonlinear Integro-Differential Equations of Convolution Type

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Abstract

Using the method of maximal monotonic (in the Browder–Minty sense) operators, we prove global theorems on the existence and uniqueness of solutions for various classes of nonlinear integrodifferential equations of convolution type in real spaces Lp, 1 < p < ∞, and present illustrative examples.

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Authors and Affiliations

  1. Chechen State Pedagogical University, Grozny, Russia

    S. N. Askhabov

  2. Chechen State University, Grozny, Russia

    S. N. Askhabov

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  1. S. N. Askhabov
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Correspondence to S. N. Askhabov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 167, Proceedings of the IV International Scientific Conference “Actual Problems of Applied Mathematics,” Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part III, 2019.

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Askhabov, S.N. Method of Maximal Monotonic Operators in the Theory of Nonlinear Integro-Differential Equations of Convolution Type. J Math Sci 260, 275–285 (2022). https://doi.org/10.1007/s10958-022-05691-5

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  • DOI: https://doi.org/10.1007/s10958-022-05691-5

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